Concentration and molecular weight effects

This chapter has proposed alternative functional forms to describe the viscoelastic functions. The two previous sections made direct tests of the validity of these forms. The functional forms predicted by the temporal scaling ansatz describe accurately the experimental measurements, once appropriate material-dependent parameters are chosen. Equivalently, the curve-fitting process reduced each set of measurements of G (a ), G co), or 7(/c) to a small number of system-dependent parameters. 

Literature studies were not planned as tests for the temporal scaling ansatz. Unsurprisingly, all studies are not equally helpful in the discussion below. The most useful experiments were conducted on one polymer system at a substantial number of concentrations, or at one concentration for homologous polymers having a substantial number of molecular weights. 

This subsection discusses the concentration and molecular weight dependences of the material-dependent parameters Gio, G20, (Oc, G, and x that 

For these systems, S is unity or close thereto at smaller c and M, and tends, but not with perfect consistency toward 0.5 at larger c and larger M, notably M above 1 MDa. For example Graessley and Segal s results(34) show 5 1 for 411 and 

860 kDa polystyrene, 255 g/1, but S 0.53 for the 1900 or 2420 kDa polymer at the same c. On the other hand, Isono and Nagasawa s results(36) on 1650 kDa poly-a-methylstyrene were all consistent with 5 = 1. The largest-M polymers reviewed here were 4 MDa xanthan(42), 5.25 MDa xanthan(21), and 7.1 MDa polystyrene(43) for all these 5 1/2. 

---

Concentration and Molecular Weight Effects. The viscosity of aqueous solutions of poly(ethylene oxide) depends on the concentration of the polymer solute, the molecular weight, the solution temperature, concentration of dissolved inorganic salts, and the shear rate. Viscosity increases with concentration and this dependence becomes more pronounced with increasing molecular weight. This combined effect is shown in Figure 3, in which solution viscosity is presented as a function of concentration for various molecular weight polymers. 

State variables of a process are the variables that uniquely specify the process at any given time (such as temperatme, monomer concentration and molecular weights). Effective monitoring and control of a process requires reliable real-time information of the state... 

So what do we have so far We have a model macromolecule that (1) has viscous drag interactions with the surrounding solvent, (2) has variable R, which describes how the macromolecule stretches and aligns when subjected to flow, (3) accounts for elasticity with a spring connector, and (4) includes the possibility for concentration and molecular weight effects through... 

Experimental values of X have been tabulated for a number of polymer-solvent systems (4,12). Unfortunately, they often turn out to be concentration and molecular weight dependent, reducing their practical utility. The Flory-Huggins theory quahtatively predicts several phenomena observed in solutions of polymers, including molecular weight effects, but it rarely provides a good quantitative fit of data. Considerable work has been done subsequentiy to modify and improve the theory (15,16). 

Mineral segregation in industry relies heavily on the selective adsorption of macromolecules onto the surfaces of those minerals that have particular industrial applications. This selectivity is governed mainly by the surface chemistry of the mineral and the type of polymer used as a flocculant. " Effectiveness of flocculation depends upon the charge, concentration and molecular weight of the polymer, and also the pH and salt concentration of the clay suspension. The bonding between the anionic flocculant polyacrylamide (PAM) and clay mineral surfaces has been effectively reviewed recently by Hocking et al and the reader is referred to this should they require an in-depth literature review. For more information on general colloidal chemistry of clay suspensions the reader is referred to the review of Luckham and Rossi." ... 

Simha and Zakin (126), Onogi et al (127), and Comet (128) develop overlap criteria of the same form but with different numerical coefficients. Accordingly, flow properties which depend on concentration and molecular weight principally through their effects on coil overlap should correlate through the Simha parameter c[ /], or cM , in which a is the Mark-Houwink viscosity exponent (0.5 < a < 0.8). If coil shrinkage, caused by the loss of excluded volume in good... 

Figure 19.2. Diagram of osmotic behavior and the effect of solute concentration and molecular weight on osmotic pressure, (a) Osmotic-pressure behavior of solutions Ais the excess pressure on the solution required to stop flow of solvent through the semipermeable membrane, (b) Effects of solute concentration and molecular weight on osmotic pressure.

Fig. 8. TEM studies of the effect of polydimethylsiloxane concentration and molecular weight on microphase development...

Wood, P.J. Beer, M.U. Butler, G. 2000. Evaluation of role of concentration and molecular weight of oat beta-glucan in determining effect of viscosity on plasma glucose and insulin following an oral glucose load. Br. J. Nutr. 84 19-23. 

Polarisation. In the event that e.e.m. takes place then the emission from the trap, excimer in the case of pure polymers, should be completely depolarised. Some time ago data was published on the emission of excimer for both polystyrene and poly(a-methyl styrene) indicating polarised emission (8) and therefore little e.e.m. More recently Phillips questioned the validity of the data and reported mesurements which suggest the excimer emission is depolarised (9 ). An experimental difference between the two sets of data is apparent - Phillips solutions were more dilute than these used in ref. 8. The range of concentrations has subsequently been extended with the results shown in Figure 1. A possible explanation for the effect of concentrations and molecular weights on the extent of polarisation of excimer emission is that the rate of rotational relaxation of this bulky entity becomes slower than the emission life-time as these two parameters increase. It is difficult to reconcile the concept of e.e.m. with polarised excimer emission. 

By decreasing monomer and initiator concentration it is possible to eliminate gelation because polymers which form gels by crystallization from solution do so at a critical concentration and molecular weight ] ). The effect of monomer and initiator concentration for the polymerization reaction at 34°C is also shown by the data in Table V. 

---